Let $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbb{R}$ be defined by $f(x) = (\log(\sec x + \tan x))^3$. Then:

If a function $g(x)$ is defined in $[-1, 1]$ and two vertices of an equilateral triangle are $(0, 0)$ and $(x, g(x))$ and its area is $\frac{\sqrt{3}}{4}$,then $g(x)$ equals :-

The range of the function $f(x) = \left[ \frac{1}{\ln(x^2 + e)} \right] + \frac{1}{\sqrt{1 + x^2}}$ is,where $[*]$ denotes the greatest integer function and $e = \lim_{\alpha \to 0} (1 + \alpha)^{1/\alpha}$.

$f(x) = \frac{x}{\ln x}$ and $g(x) = \frac{\ln x}{x}$. Identify the $CORRECT$ statement.

If the graph of a non-constant function $f(x)$ is symmetric about the point $(3,4)$,then the value of $\sum\limits_{r = 0}^6 {f(r) + f(3)}$ is equal to

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers. Let $f(x) = \alpha x^5 + \beta x^3 + \gamma x, x \in \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be such that $g(f(x)) = x$ for all $x \in \mathbb{R}$. If $a_1, a_2, a_3, \dots, a_n$ are in arithmetic progression with mean zero,then the value of $f(g(\frac{1}{n} \sum_{i=1}^{n} f(a_i)))$ is equal to.